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In today's busy life, no one has sufficient time to buy or bargain any type of products. It is common in such cases that customers, who are looking for purchasing a certain product, will be willing to substitute with a comparable product when facing a stock-out, rather than visiting a different store to bargain the original product. In this article, we study an inventory control problem in which demand is fulfilled by using two similar substitutable items. Retailer fulfilled demand of one product by other substitutable product when stock-out of the one of them. We consider inventory levels of both of the items and time dependent demand. The orders for both products are placed at the same time. Our objective is to maximize joint profit for two substitutable deteriorating items with respect to cycle time and a time at which one product is stock-out.The numerical analysis is carried out based on the analytical results. The critical inventory parameters are computed for the decision maker.

In particular business transactions, the supplier usually provides an admissible delay in settlement to its vendor to encourage further sales. Additionally, the demand for the commodity is inversely proportional to the function of the sales price, which is non-linear and, in some situations, a holding cost rises over time. Moreover, many goods often deteriorate consistently and shall not be sold after their expiration dates. This study analyses a model for perishable products with a maximum life span with price-dependent demand and trade credit by assimilating these variations and under the supposition of time-varying holding cost. Furthermore, to diminish the rate of deterioration, investment for preservation technology is often taken into account beforehand. Based on real-life circumstances, shortages are admitted and backlogged partially, with an exponential rise in wait time before the new good emerges. The key ambition is to calculate the optimum investment under preservation, sales price, and cycle time using the classical optimization algorithm to maximize the vendor’s net profit. Additionally, to clarify the outcomes, the numerical illustrations are addressed, and the sensitivity analysis of significant parameters is eventually implemented.

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